Pennant Fever Review Adam Johnson Nate Levin Ian Olsen.

Slides:

Advertisements

Similar presentations

Binomial Theorem 11.7.

Advertisements

Methods of Enumeration Counting tools can be very important in probability … particularly if you have a finite sample space with equally likely outcomes.

Chapter 6 – Polynomial Functions

Warm-Up Complete in notes.

Warm Up Multiply. 1. x(x3) x4 2. 3x2(x5) 3x7 3. 2(5x3) 10x3 4. x(6x2)

Chapter 8 Counting Techniques PASCAL’S TRIANGLE AND THE BINOMIAL THEOREM.

6.5 Binomial Theorem 1 Previously, we learned patterns for squaring and cubing binomials. (x+y) 2 = x 2 + 2xy + y 2 (x+y) 3 = x 3 + 3x 2 y + 3xy 2 + y.

Counting principle and permutations

Multiplying Integers.

Basic Laws Of Math x

Use Combinations and the Binomial Theorem (continued)

Copyright © 2011 Pearson, Inc. 9.2 The Binomial Theorem.

Notes 9.2 – The Binomial Theorem. I. Alternate Notation A.) Permutations – None B.) Combinations -

What does Factorial mean? For example, what is 5 factorial (5!)?

The Binomial Theorem. Powers of Binomials Pascal’s Triangle The Binomial Theorem Factorial Identities … and why The Binomial Theorem is a marvelous.

Chapter  Determine how many different possibilities are possible:  1. There are 3 different ice cream flavors and 5 different toppings. You.

Algebra 2.  Warm Up  A monomial is an expression that is either a real number, a variable or a product of real numbers and variables.  A polynomial.

Notes Over 12.2 Finding Combinations 1. An ice cream shop has a choice of 10 toppings. In how many ways can you choose 3 different toppings for your ice.

Introduction Binomial Expansion is a way of expanding the same bracket very quickly, whatever power it is raised to It can be used in probability, in.

Lesson 6.8A: The Binomial Theorem OBJECTIVES:  To evaluate a binomial coefficient  To expand a binomial raised to a power.

Arrangements How many ways can I arrange the following candles?

9.5 The Binomial Theorem Let’s look at the expansion of (x + y)n

Binomial Theorem & Binomial Expansion

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

2-6 Binomial Theorem Factorials

A binomial is a polynomial with two terms such as x + a. Often we need to raise a binomial to a power. In this section we'll explore a way to do just.

7.1 Pascal’s Triangle and Binomial Theorem 3/18/2013.

Pg. 606 Homework Pg. 606 #11 – 20, 34 #1 1, 8, 28, 56, 70, 56, 28, 8, 1 #2 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1 #3 a5 + 5a4b + 10a3b2 + 10a2b3.

Essential Questions How do we multiply polynomials?

Algebra 2 CC 1.3 Apply the Binomial Expansion Theorem Recall: A binomial takes the form; (a+b) Complete the table by expanding each power of a binomial.

Algebra - only covering Aiden. Learning Objectives 2.2 When a polynomial is given You will need to be able to tell yourself The highest degree.

Multiplying Binomials

Binomial Theorem and Pascal’s Triangle.

2.1 Patterns of Multiplication

Chapter 12.5 The Binomial Theorem.

Classifying, Adding, and Subtracting Polynomials

Least Common Multiple.

Today’s topics Counting Reading: Sections , 4.4 Upcoming

The Binomial Theorem.

Section 9-5 The Binomial Theorem.

The Binomial Theorem Ms.M.M.

The Binomial Theorem 8.5.

A quick and efficient way to expand binomials

4.2 Pascal’s Triangle and the Binomial Theorem

10.2b - Binomial Theorem.

Use Combinations and the Binomial Theorem

Objectives Multiply polynomials.

4-2 The Binomial Theorem Use Pascal’s Triangle to expand powers of binomials Use the Binomial Theorem to expand powers of binomials.

Essential Questions How do we use the Binomial Theorem to expand a binomial raised to a power? How do we find binomial probabilities and test hypotheses?

Use Pascal’s triangle to expand the expression (3 x - 2 y) 3

The Converse of the Pythagorean Theorem

Classifying, Adding, and Subtracting Polynomials

The Binomial Theorem.

How do I Multiply Polynomials? How do I use Binomial Expansion?

Compare the 2 diagrams below

Classifying, Adding, and Subtracting Polynomials

Multiplying binomials the Break up out of jail method

Chapter 12 Section 4.

The Binomial Theorem.

Summary What have we learned?.

N! 4 x 3 x 2 x 1 = 24.

Unit 5 Polynomial Operations

Multiplying binomials

9.2 The Binomial Theorem.

Two hungry Math 160 students are waiting in line at Chipotle

Warm Up 1. 10C P4 12C P3 10C P3 8C P5.

Section 11.7 The Binomial Theorem

Multiplying binomials

Algebra 2 Ch.6 Notes Page 23 P Pascal's Triangle and The Binomial Theorem.

Presentation transcript:

Pennant Fever Review Adam Johnson Nate Levin Ian Olsen

Unit Problem  The good guys and the bad guys each have 7 games to play. Based on each of their winning records (.62 good guys and.6 bad guys) we must determine the chances each team has to win the pennant.

Key Topics  Combinations  Permutations  Pascal’s Triangle  Factorials  Binomial Theorem

Factorials  Multiplication pattern  Sign is “!”  Multiply the coefficient of “!” by every whole number below it, excluding numbers zero and below.  4!=4*3*2*1=24

Combinations  nCr  n!/(n-r)!*r!  Order doesn’t matter  Bowls of ice cream  Answer question #1 on worksheet now

Question #1  12C1 x 7C1 x 4C1 x 5C1=?  12x7x4x5=1680  When r value is equal to one, the final answer of the value is equal to the n value  (12!/(12-1)!*1!)*(7!/(7-1)!*1!)*etc…  5C1=5  5*4*3*2*1=120  120/4!=5

Permutations  nPr  n!/(n-r)!  Order does matter  Cones of ice cream  Answer question #4 on worksheet now

Question #4  22P7=?  22!/(22-7)!=859,541,760  22!=1.12E21  Answer question #2

Question #2  Explain the difference between 10P7 and 10C7  Well P will obviously be larger as the order of the combinations matter, increasing the total number of possibilities.

Question #2 (Continued)  We can see the steps that are different in the previous slide that make 10P7 and 10C7 different.  Due to the difference in order mattering or not, the final answer will change drastically.

Pascal’s Triangle  Shows the binomial coefficient  Shows nCr values

Binomial Theorem  Finds the coefficients of binomial  Answer question #8

Question #8  (2X+3)^5